报告人：黄飚 副教授（中国科学院大学）

题目：Universal distribution of many-body localized eigenstates and selection-rule-related gap ratios（多体局域化本征态的普适分布及与选择定则相关的能隙比）

时间：2025年6月25日 下午16:00

地点：理工楼1226

联系人：程晨

报告摘要：

Recent studies of many-body localization (MBL) have highlighted the important but rarely explored regime with strong disorders, which were believed to reside deeply inside the localized side. However, resonances among eigenstates may have already destabilized the localization as fueled by the so-called avalanche mechanism. Understanding how these resonances arise and quantifying their universal behaviors analytically is desirable to unveil the nature of MBL in such regimes. This talk will introduce an analytical theory to quantitatively calculate the universal eigenstate distributions in Fock space. Our approach distinguishes from the previous analytical framework by explicitly incorporating a probability distribution function into the Fock space perturbation series. As a result, our closed-form formula directly predicts the values of physical quantities, such as the distribution of inverse-participation-ratio for eigenstates, that would be obtained in numerics after averaging over large numbers of disorder realization. It is found that pairwise resonance occurs in such strongly disordered regimes for eigenstates, which leads to two different scaling behaviors for eigenstates at the same parameter point. Moreover, based on our new analytical framework, we introduce the unconventional level spacing statistics (LSS) for non-consecutive levels related by Fock space selection rules, which sensitively capture resonance-induced level repulsions that already occur deep inside the localized regime. The non-consecutive gap ratios therefore show Gaussian Orthogonal Ensemble behaviors. This is in sharp contrast to conventional LSS for consecutive levels showing Poissonian distributions with the same parameters. Our analytical framework opens the door to viably calculating universal features for eigenstates in a strongly disordered interacting system, and points out a practical way to check selection-rule-related non-consecutive level spacings that can be essential in proximity to integrable points.

近期关于多体局域化的研究揭示了强无序体系这一重要但少有探索的范畴，人们曾认为强无序体系处于局域化区域的深入。然而，本征态之间的共振可能已经像所谓的雪崩机制所推动的那样，破坏了局域化的稳定性。要理解这些共振如何产生并解析地量化其普适行为，对于揭示此类体系中MBL 的本质至关重要。本次报告将介绍一种解析理论，用于定量计算福克空间(Fock space) 中的普适本征态分布。我们的方法区别于之前的解析框架之处在于，明确地将一个概率分布函数纳入到福克空间的微扰级数中。因此，我们的闭式表达式能够直接预测物理量的取值，例如本征态的逆参与率 (inverse-participation-ratio) 的分布，这些物理量通常是在大量无序构型的平均后通过数值计算得到的。研究发现，在此类强无序体系中，本征态之间发生了配对共振，这导致了在同一参数点处本征态的两种不同的标度行为。此外，基于我们新的解析框架，我们引入了适用于由福克空间选择定则关联的非连续能级的非传统能级间距统计(LSS)。这种新方法灵敏地捕捉了在局域化区域深处已然发生的、由共振引起的能级排斥。因此，这些非连续能级的能隙比展现出高斯正交系综 (Gaussian Orthogonal Ensemble, GOE) 的行为。这与用于连续能级的传统能级间距统计形成鲜明对比，后者在相同参数下显示泊松 (Poissonian) 分布。我们的解析框架为切实计算强无序相互作用体系中本征态的普适特征开启了大门，并指出了一种实用的方法来检查与选择定则相关的非连续能级间距，这在接近可积点时可能至关重要。

个人简介：

Dr. Biao Huang obtained PhD degree in 2016 from The Ohio State University, after which he was a postdoctoral researcher at University of Pittsburgh from 2016-2019. He went to Max-Planck-Institute for the Physics of Complex Systems in Germany from 2019-2021 as a guest scientist. In 2021, he joined the faculty of Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences. His research focuses on systems far from equilibrium, which can host many interesting dynamical phenomena absent from static counterparts, such as many-body scars, discrete time crystals, and the anomalous Floquet topological insulators.

黄飚博士于 2016 年在美国俄亥俄州立大学获得博士学位。此后，于 2016 至 2019 年间在美国匹兹堡大学担任博士后研究员；2019 年至 2021 年，作为访问科学家 (Guest Scientist) 工作于德国马克斯・普朗克复杂系统物理研究所；2021 年加入中国科学院大学卡弗里理论科学研究所任职。其研究聚焦于远离平衡态的系统。这类系统展现出许多其静态平衡系统中所不存在的有趣动力学现象，例如多体疤痕态、离散时间晶体和反常Floquet拓扑绝缘体。